Strong’s definition of the word line is a cord, thread (twisted) and comes from the Hebrew root H6617 meaning to struggle or (figuratively) be (morally) tortuous:-(shew self) froward, shew self unsavory, wrestle.
The word flax is linen, fiber used as a material for garments and comes from the root 6580 meaning folly, weakness, stupidity, as in the sense of comminuted.
2 Answers
Using Young's Concordance, the Hebrew word pathil occurs here (and nowhere else in the Hebrew scriptures). It means 'ribbon, thread', and is translated as 'thread'.
Therefore, Young's Literal Translation speaks of this vision of a man appearing as brass: "...and a thread of flax in his hand, and a measuring-reed, and he is standing at the gate." It is clear from the many verses following, regarding measuring, that the reed is used for measuring buildings.
Then, in Ezekiel 47:3, the same visionary man is said to "have a line in his hand", but no mention now of the measuring-reed. The Hebrew word is qeveh, which means 'a line, rule'. YLT shows this line being used to measure depths of water.
As for flax, in Ezekiel 40:3, it is the Hebrew word pishteh. This means, 'flax, linen'. It would seem that the line of flax in Ezekiel 40:3 is one thing (a thread or cord of linen), while in Ezekiel 47:3 the line in the hand might not be made of cloth, but a firmer material that can be used for putting down into a body of water so as to get the depth of it. This point is confirmed in The Companion Bible notes (see page 1164 and the appendix for 40:3, and page 1175. )
As all of this is visionary, there might be some mileage in pursuing symbolic meanings for the subtle nuances of the various Hebrew words in those two verses, and I hope a Hebrew scholar will oblige.
Adding to @Anne's answer:
Rashi points out the function of the the two measuring methods
with a linen cord in his hand For measuring land, there is nothing better than linen cord.
and a measuring rod with which to measure the thickness of the wall and the length and width of the gates.
The Abarbanel, translated by ChatGPI, explains the importance of the “visionary man”:
"And he remembered that he was brought there and saw a man whose appearance was like that of copper, meaning its brightness and clarity, as it is said (above 1:7), 'and they are shining like the brightness of copper.' And that awesome angel was measuring the building, and therefore he had a flaxen thread and a measuring rod with a cord. With the thread, he measured a large measure on the ground, and with the rod, he measured a smaller measure. The meaning he showed him was the future building of the house that will comfort Israel, who are in exile, that their descendants will return to the land, settle in it securely, and rebuild the Temple, greater than it was at first. And he revealed to him that the future building of the house will not be like the second Temple, which was by the will of the people and according to the measure given to them by the King of Persia, but it will be by the decree of the eternal word. Therefore, he showed him the man who was standing over the builders, measuring the length and width, because everything will be from the Lord, from the heavens."